transient stability analysis of vsc hvdc transmission...

Turk J Elec Eng & Comp Sci

(2015) 23: 1834 – 1852

c⃝ TUBITAK

doi:10.3906/elk-1404-214

Turkish Journal of Electrical Engineering & Computer Sciences

http :// journa l s . tub i tak .gov . t r/e lektr ik/

Research Article

Transient stability analysis of VSC HVDC transmission with power injection on

the DC-link

Agha Francis NNACHI1,∗, Josiah MUNDA1, Dan Valentine NICOLAE1, Augustin Mabwe MPANDA2

1Department of Electrical Engineering, Tshwane University of Technology, South Africa2Graduate School of Electronics and Electrical Engineers (ESIEE), Amiens, France

Received: 12.04.2014 • Accepted/Published Online: 22.06.2015 • Printed: 30.11.2015

Abstract: The utilization of a DC-link transmission corridor of embedded VSC HVDC for a DC power injection from

renewable energy sources to increase the power flow capability and AC network stability support is a promising technology.

However, DC faults on the DC transmission line are likely to threaten the system’s operation and stability, especially

when the DC power injection exceeds certain limits. A DC single line-to-earth fault is the most likely fault scenario

and its effect on the VSC HVDC operation will depend on the earth-loop impedance. Adding an injection point on the

DC-link will reduce the earth-loop impedance, hence imposing a danger of increasing the earth fault current. Therefore,

in this paper, a VSC HVDC with a DC power injection on the DC-link is studied, the DC-line-to-earth fault is analyzed

in the time domain, and its effects on the DC and AC sides of the system are presented. The analysis is based on a

developed state-space representation of the system under a single-line-to earth fault. The zero-input zero-state (ZIZS)

response is used to find the solution of the state-space representation. In order to correlate the state-space solution with

a simulation, the system is modeled in MATLAB/Simulink. Interestingly, it was observed that a quick recharging of the

DC-link capacitor due to a power injection created an additional damping of the postfault oscillations of the AC-side

power angle and the DC-side voltage and power oscillations, hence enhancing transient stability.

Key words: Transient stability, voltage source converter, DC power injection

1. Introduction

Embedding a voltage source converter high voltage direct current (VSC HVDC) in AC networks opens up new

possibilities to enhance the operation of smart transmission grids with improved transient stability, increased

power transfer capability, capacity utilization, and delivery efficiency [1]. Moreover, VSC HVDC (HVDC plus

or HVDC light) with a long DC transmission link in power systems will facilitate power injections and tap-offs

on the DC-link resulting in multiterminal systems for more power transfer capability, support, and supply to

disperse rural or electrification loads [2]. The technology of multiterminal HVDC systems has been considered

in the literature [3–7] with the view of control coordination among all terminal stations.

However, most of the VSC HVDC systems are two-terminal or point-to-point connection. Here are

several examples: 300 MW, 350 kV Caprivi link of Namibia; 400 MW, 200 kV US-East Bay Oakland; 400

MW, 150 kV NordE.ON1 Germany; 350 MW, 150 kV Estlink Estonia Finland-Espoo; 200 MW, 150 kV Murray

link Australia; etc. These two-terminal DC-links were generally not designed for the connection of distributed

generators [8].

∗Correspondence: [email protected]

1834

NNACHI et al./Turk J Elec Eng & Comp Sci

Connecting a generation scheme to any transmission or distribution system entails taking into consider-

ation certain technical issues such as [9,10]: the thermal rating of the equipment, system fault levels, stability,

reverse power flow capability, line-drop compensation, steady-state voltage rises, losses, power quality (such as

flicker, harmonics), and protection. The main requirement for a DC power injection on the DC-link transmis-

sion corridor of VSC HVDC is injecting a strictly locally controlled power that will not interfere with the main

HVDC system control.

In [11], using the principle of uniform loading, a DC power injection limit that could be accepted at any

point on the DC-link of a VSC HVDC transmission corridor without affecting the main VSC HVDC control was

proposed. However, there is a need to investigate the transient stability of this system during power injection.

The degree of transient stability will depend on the location and nature of the disturbance in addition to the

initial operating point [12].

Faults may occur at the AC side of the VSC HVDC transmission or on the DC-link transmission corridor,

and their stability responses will differ. In [13], it was indicated that if a severe disturbance threatens the system’s

transient stability on the AC side, the VSC HVDC can help maintain a synchronized power-grid operation by

fast power run-up or run-back control functions. On the other hand, VSCs are vulnerable to DC cable short-

circuits and ground faults due to a high discharge current from the DC-link capacitance. Therefore, DC faults

on the DC transmission line are likely to threaten the system’s operation and stability, especially when the DC

power injection exceeds a certain limit.

The effect of this DC-line-to-earth fault on the VSC HVDC operation will also depend on the earth-loop

impedance. Various works [14–16] have been carried out on power injection or tapping on the DC-link of the

VSC HVDC transmission, but the transient stability of the system under DC fault conditions needs to be

addressed. Moreover, most researchers [17–19] have based their DC fault analyses on simulations alone.

In this paper, a time-domain transient stability analysis of VSC HVDC during power injection is pre-

sented. In the analysis, a state-space representation of a DC-link single-line-to-ground fault during DC power

injection is developed. In addition, the zero-input zero-state (ZIZS) response is used to find the solution of the

state-space representation. In order to correlate the time-domain solution with a simulation, a two-terminal

VSC HVDC with a DC link power injection is developed in the MATLAB/Simulink environment for this study.

2. A VSC HVDC system with DC-power injection

Figure 1 shows a typical embedded VSC HVDC that consists of two main converter stations; one station operates

as a rectifier and the other operates as an inverter station. The coordination of active power control between

the stations is realized by designing only one converter that controls the DC-side voltage, whereas the other

converter regulates the active power. A constant DC voltage control gives a slack bus, which will result in an

automatic balance of active power flow between stations [20]. The injection station has its own local control,

which should not interfere with the main converter controls. The generator is in stable operation at a phase

angle of δ1 compared with the VSC bus, i.e. the voltage at generator bus E1 is leading the voltage at converter

bus U1 by an angle of δ .

Introducing DC power on the DC-link and increasing its power injection could reach such an extent that

the direction of power flow of the main system could be reversed, causing a net voltage rise at the injection bus

and leading to instability.

1835


1∠ 1

ℎ1∠ 1 1∠0 2∠0

ℎ2∠ 2

2∠ 2

Figure 1. A VSC HVDC with a single machine connected infinite bus having a DC power injection station on the

DC-link.

The proposed injection limit is a function of the control parameters of the main converter and the DC-link

parameter as shown in Eq. (1).

P inj limit = εP ref , (1)

where

ε = −Udcmax (Udcmax − Udcref )

rx+

(1− x

2L

)Udc2Idc2

= −Udcmax (Udcmax − Udcref )

rx+(1− x

2L

) U2E2

Xthsinδ2.

Pinj limit = the maximum power injection for unity reference power of the main control

Udcmax = the upper voltage regulation limit in p.u. specified in the control

Udcref = the reference voltage in p.u.

r = resistance per kilometer of the line

x = the distance to the injection station from bus 1

L = total length of the DC-link

U2 = converter AC2 output voltage

E2 = AC2 bus voltage

Xth = the thevenin equivalent reactance of the AC system

Udc2 = p.u. upper voltage regulation (limit in p.u specified in the inverter control)

Idc2 = Irated = p.u. current reference limit (current set point specified in the inverter control)

3. VSC system DC faults

It is quite true that numerous precautions are taken to ensure the protection of HVDC cables against line

faults. Such protections include cable armoring and insulation for submerged cables. However, human and

natural factors such as cable deterioration, cable aging, weather, and ocean currents and waves can stress the

cable, resulting in insulation breakdowns or potentially broken cables [21]. DC line faults could be line-to-line

or line-to-earth faults. However, a single line-to-earth fault is a more likely fault scenario than a line-to-line

fault. The occurrence of a DC fault on the DC link of a VSC HVDC will result in fast discharging of the

DC-link capacitors and a large AC-side current flowing to the DC link fault point through the antiparalleling

(freewheeling) diodes of the converter [22].

1836


4. Transient analysis of a single DC-line-to-earth fault

4.1. State-space representation during a DC power injection

In this section, a transient response from a state-space representation of a single DC-line-to-earth fault during

a DC power injection is presented.

The behavior of the system (Figure 2) under earth fault depends on the earth-loop impedance. As a

result, the analysis of the single-line earth fault depends on the earthing system of both the main stations and

the injection station. The possible earthing points are the neutral of the step-up transformer, the earthing of

the DC link midpoint, and the earthing of the injection station. An earth fault will form an earth loop with

the earthing of these earthing points [22].

Figure 2. A voltage source converter HVDC with an injection station on the DC-link.

When a line-to-earth fault occurs, the voltage at the point of fault drops significantly, resulting in a high

DC fault current. This rise in the DC fault current will result in blocking the IGBTs and hence a rise in the

AC fault current. The blocked voltage source will act like an uncontrolled rectifier with the DC-link voltage

changing to the rectified voltage, so the current will flow through the diodes as shown in Figure 3. Figure 4

shows the equivalent circuit for the VSC HVDC with a DC power injection under a DC line to earth fault.

The earth fault resistance Rf is usually from ohms to hundreds of ohms [23]. The line is modeled by a lumped

parameter R-L element.

Figure 3. An equivalent circuit of the VSC as a result of blocking the IGBTs.

In order to analyze the response of the system, zero-input and zero-state solutions of the system can be

found if the state space representation is known.

Therefore, the state space of the equivalent circuit can be derived in state space as follows:

1837


Figure 4. An equivalent circuit of the VSC HVDC with a power injection on DC-link during a DC-line earth fault.

Applying Kirchhoff’s laws on each node:

Node 1:

ic1 = iLac − iLdc1 ⇒ C1dvc1dt

= −iLdc1 + iLac (2)

vLdc1 = vc1 − vci − vRdc1 ⇒ diLdc1

dt=

1

Ldc1(vc1 − vci −Rdc1 iLdc1 ) ; (3)

Node 2:

ic2 = iLdc1 + iinj − iLdc2 ⇒ C2dvcidt

= iLdc1 + iinj − iLdc2

⇒ dvcidt

=iLdc1 + iinj − iLdc2

C2(4)

vLdc2 = vci − vRf − vRdc2 ⇒ Ldc2diLdc2

dt= vci − iLdc2 (Rdc2 +Rf )

⇒ diLdc2

dt=

vciLdc2

− iLdc2(Rdc2 +Rf )

Ldc2(5)

vLac = −vc1 + vg a,b,c ⇒ LacdiLac

dt= −vc1 + vg a,b,c. (6)

Since the aim here is to monitor the response of the DC-link voltages and currents and the AC current, the

state variables vc1, vciiLdc1, iLdc2, iLac can be solved analytically in the time domain or s-domain. Hence, from

Eqs. (2)–(6), the state space of the system is defined by the following equation:

x (t) = Ax (t) +Bu (t)y (t) = Cx (t) +Du (t)

, (7)

where:

x is the state vector [vc1, vci, iLdc1, iLdc2, iLac]T,

A is the state matrix

00

1Ldc1

0− 1

Lac

00− 1

Ldc11

Ldc2

0

− 1C1

1Ci

Rdc1

Ldc1

00

0− 1

Ci

0(Rdc2+Rf )

Ldc2

0

1C1

0000

,

1838


B is the input matrix

00000

01/Ci

000

00000

00000

00001/Lac

,

u is the input [0, iinj , 0, 0, vg a,b,c]T,

C is the output matrix

10000

01000

00100

00010

00001

,

D is the direct transition (or feed through) matrix [0] , and y is the output.

4.2. Solution of the state space

Having the state matrix, the zero-input (Z i) and zero-state (Zs) solution of the system can be found. The

zero-input solution is the response of the system to the initial conditions, with the input set to zero. The

zero-state solution is the response of the system to the input, with initial conditions set to zero. The complete

response is simply the sum of the zero-input and the zero-state responses.

To find the Z i solution to the system defined in state space, the zero-input problem is given by:

xzi = Axyzi = Cx

, (8)

with a known set of initial conditions, x (0−).

The state transition matrix is an important part of both the zero-input and the zero-state solutions of

the state space. The state transition matrix in the Laplace domain, ??(s), is defined as:

Φ (s) = (sI −A)−1

, (9)

where I is the identity matrix.

The time-domain state transition matrix, φ (t), is simply the inverse Laplace transform of Φ (s).

The first thing is to solve for x (t) by taking the Laplace transform and solving for X (s):

sXzi (s)− x(0−

)= AXzi (s) (10)

sXzi (s)−AXzi (s) = x (0−) i.e. sIXzi (s)−AXzi (s) = x (0−)

(sI −A)Xzi (s) = x(0−

)Xzi (s) = (sI −A)

−1x(0−

). (11)

Substituting Eq. (9) in Eq. (11),

Xzi (s) = Φ(s)x(0−

). (12)

1839


Since x (0−) is a constant multiplier, the inverse Laplace Transform is simply

xzi (t) = φ (t)x(0−

). (13)

Therefore, the solution for y(t) is found in a straightforward way from the output equation:

yzi (t) = Cxzi (t) = Cφ (t)x(0−

)(14)

Next will be to find the zero-state response of the system. In the Laplace domain the response is found by first

finding the transfer function of the system:

H (s) =Y (S)

U (S)= CΦ(s)B +D, (15)

Yzs (S) = H (s)U (s) . (16)

In the time domain, Eq. (16) (multiplication in the Laplace domain) yields:

yzs (t) = h (t) ∗ U (t) = (Cφ (t)B +D) ∗ u (t) . (17)

The asterisk denotes convolution.

Then the complete response is simply the sum of Eqs. (14) and (17):

yc (t) = yzi (t) + yzs (t) . (18)

Table 1 shows the parameters used for plotting the solutions (Eqs. (14), (17), and (18)).

Table 1. Parameters used for plotting the solution in the MATLAB environment.

Elements ValueLength of DC-link 950 kmDistance from VSC1 bus to injection station bus 475 kmDC-bus capacitor C1 24 µFInjection DC-bus capacitor Ci 12 µFDC-line inductance Ldc1 0.00159 × 475 HDC-line inductance Ldc2 0.00159 × 125 HDC-line resistance Rdc1 0.00139 × 475 ohmDC-line resistance Rdc2 0.00139 × 125 ohmEarth-fault resistance Rf 0.05 ohmAC line inductance Lac 0.0487

AC phase voltage Vga 400/√3 kV

Initial conditions x (0−) = [6500;1200; 0; 0;0]

Figures 5–8 show the zero-input, zero-state, and combined state solutions or responses of the state

variables vc1, vciiLdc1, iLdc2, iLac obtained from Eqs. (14), (17), and (18), respectively.

1840


0 2 4 6 8 10 12–20

0

20

40

60

80

100

120

Time (s)

DC

Bu

s1 V

olt

age

(kV

)

Zero Input Response

0 2 4 6 8 10 12–6

–5

–4

–3

–2

–1

0

1x 10 4

Time (s)

DC

Bu

s 1

Vo

ltag

e (k

V)

Zero State Response

(a) (b)

0 2 4 6 8 10 12–6

–5

–4

–3

–2

–1

0

1x 10 4

Time (s)

DC

Bu

s1 V

olt

age

(kV

)

Combined Response

(c)

Figure 5. Response of DC bus 1 voltage: a) zero-input response, b) zero-state response, c) combined response.

Figure 5a shows the zero-input response of DC-bus 1 voltage and it can be seen that the capacitor is

first charged up to 120 kV due to the initial condition and completely discharged. Figures 5b and 5c show the

complete draining of DC bus 1 voltage. Figure 6, which shows the response of the injection station bus voltage,

depicts a fast charging up to 800 kV due to the power injection and later discharging completely due to the

1841


line-to-earth fault. Figure 7 shows a fast rise in the DC inductor current, which is a result of the reduced fault

loop impedance.

0 2 4 6 8 10 12–100

0

100

200

300

400

500

600

700

800

Time (s)

DC

Bu

s–i

Vo

latg

e (k

V)

Zero Input Response

0 2 4 6 8 10 12–7

–6

–5

–4

–3

–2

–1

0

1x 10 4

Time (s)

DC

Bu

s–i

Vo

latg

e (k

V)

Zero State Response

(a) (b)

0 2 4 6 8 10 12–7

–6

–5

–4

–3

–2

–1

0

1x 104

Time (s)

DC

Bu

s–i

Vo

ltag

e (k

V)

Combined Response

(c)

Figure 6. Response of the injection bus voltage: a) zero-input response, b) zero-state response, c) combined response.

More interestingly, Figures 8a–8c show a fast rise in the AC current, which is a result of severe overcurrents

due to the discharge of the DC-link capacitances as shown in Figure 8c. Therefore, the converter is defenseless

1842


against DC faults and it is imperative that the protection system, both on the DC and the AC side of the

HVDC, should be very fast, reliable, and sensitive during DC system faults.

0 2 4 6 8 10 12–16

–14

–12

–10

–8

–6

–4

–2

0

2

Time (s)

DC

In

du

cto

r cu

rren

t (k

A)

Zero Input Response

0 2 4 6 8 10 120

2

4

6

8

10

12

14x 105

Time (s)

DC

in

du

cto

r cu

rren

t (k

A)

Zero State Response

(a) (b)

0 2 4 6 8 10 120

2

4

6

8

10

12

14x 10 5

Time (s)

DC

in

du

cto

r C

urr

ent

(kA

)

Combined Response

(c)

Figure 7. Response of the DC inductor current: a) zero-input response, b) zero-state response, c) combined response.

1843


4.3. State-space representation when there is no DC power injection station

When there is no power injection station, the earth-loop form shared between the injection station, the DC cable,

and the AC source is eliminated. This will lead to an increased impedance of the earth-loop, thereby reducing

the earth fault current. In this case, the state space reduces to 3 × 3 with a state vector x = [vc1, iLdc, iLac]T,

0 2 4 6 8 10 12–2

0

2

4

6

8

10

Time (s)

AC

In

du

cto

r cu

rren

t (k

A)

Zero Input Response

0 2 4 6 8 10 120

2

4

6

8

10

12

14x 10 5

Time (s)

AC

in

du

cto

r cu

rren

t (k

A)

Zero State Response

(a) (b)

0 2 4 6 8 10 120

2

4

6

8

10

12

14x 10 5

Time (s)

AC

In

du

cto

r cu

rren

t (k

A)

Combined Response

(c)

Figure 8. Response of the AC inductor current: a) zero-input response, b) zero-state response, c) combined response.

1844


A =

0 − 1C1

1C1

1Ldc

−(Rdc2+Rf )Ldc2

0

− 1Lac

0 0

, B =

0 0 00 0 00 0 1/Lac

, u = [0, 0, vg a,b,c]T, C =

1 0 00 1 00 0 1

,

D is the direct transition (or feed through) matrix [0] , and y is the output.

0 2 4 6 8 10 12-10

-8

-6

-4

-2

0

2

4

6

8

10

Time (s)

DC

Bus1

Volt

age

(kV

)

Zero Input Response

0 2 4 6 8 10 12-6

-5

-4

-3

-2

-1

0

1x 10 4

Time (s)

DC

Bus1

Volt

age

(kV

)

Zero State Response

(a) (b)

0 2 4 6 8 10 12-6

-5

-4

-3

-2

-1

0

1x 104

Time (s)

DC

Bus1

Volt

age

(kV

)

Zero State Response

(c)

Figure 9. Response of DC bus-1 voltage: a) zero-input response, b) zero-state response, c) combined response.

1845


Figures 9 and 10 show the ZIZS solution of the system. Figure 9a shows an oscillation of the DC bus

voltage at a reduced magnitude when compared with Figure 6a. From Figures 9b and 9c, it can be observed

that there is a fast and complete drainage of DC bus-1 voltage. Figure 10 shows a fast rise in the AC current

with a lesser magnitude of the zero-input response when compared with Figure 8, and this is due to the fact

that the earth-loop impedance has increased.

0 2 4 6 8 10 12–0.2

–0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Time (s)

AC

In

du

cto

r cu

rren

t (k

A)

Zero Input Response

0 2 4 6 8 10 120

2

4

6

8

10

12

14x 10

5

Time (s)

AC

in

du

cto

r cu

rren

t (k

A)

Zero State Response

(a) (b)

0 2 4 6 8 10 120

2

4

6

8

10

12

14x 10

5

Time (s)

AC

in

du

cto

r cu

rren

t (k

A)

Combined Response

(c)

Figure 10. Response of the AC inductor current: a) zero-input response, b) zero-state response, c) combined response.

1846


5. Simulation

To demonstrate the operation of a VSC HVDC with DC power injection under a DC single-line-to-earth fault,

a model was developed in the MATLAB/Simulink environment.

Table 2 shows the simulation parameters of a typical 300 MW, 350 kV Caprivi VSC HVDC transmission

system used for the modeling in Simulink.

Table 2. Simulation parameters.

Data ParametersPower rating 300 MWOverload rating in monopolar mode 350 MWNo. of poles 1AC voltage Gerus: 400 kV; Zambezi: 330 kVDC voltage 350 kVCoupling transformer on both sides (Gerus and Zambezi) 315 MVALength of overhead DC line 950 kmSwitching frequency of converter valve 1150 kHz

The essence of the simulation is to show the effect of DC power injection on both DC-side and AC-side

transient stability. During the simulation, a comparison is made on the DC fault analysis for when there is no

power injection and when there is a DC power injection above and below the injection limit.

From the control setting parameters of the VSC HVDC transmission system in Simulink with a DC-link

of 950 km, the following parameters were used to determine the injection limit:

Udcmax = 1.05 pu; Udcref = 0.95; Udc2 = 1.05 pu; Idc2 = 1.1 pu; r = 0.0139Ω km, Pref = 0.63.

Substituting the control and DC-link parameters in Eq. (1), the DC power injection limit can be calculated as

0.54 p.u. (162 MW).

During the simulation, a single-line-to-earth fault was applied on the positive line of the DC-link at 1.8

s, and the DC breaker opens at 1.9 s and closes at 2 s after the fault has been cleared in 1.92 s.

5.1. DC-side transient stability

Figures 11 and 12 show the DC-side transient response of the power and voltage, respectively. Comparing

Figures 11a and 11b, it could be observed that the postfault power oscillation damped faster during power

injection.

However, in Figure 11c, during power injection above the limit, PDC1 is seen to be reduced to 177 MW,

showing that there is a reverse power flow to station 1, hence violating power stability.

Comparing Figures 12a and 12b, it can be seen that the oscillation of the voltage damped faster during

the scenario of power injection below the limit, hence improving voltage stability in the postfault period. During

power injection above the limit, it can be seen from Figure 12c that although the oscillation is damped faster,

UDC1 and UDC2 are 387 kV and 371 kV respectively—more than the upper voltage regulation limit in p.u.

specified in the control, and hence violating the voltage stability of the system.

1847


1.5 1.8 1.9 2 2.5 2.8 3–400

–180

–100

0

100

190

300

400

Time (s)

DC

Po

wer

(M

W)

PDC1

PDC2

1.5 2 2.5 3–400

–300–280

–200

–100

0

100

161190

250

300

400

Time (s)

DC

Po

wer

(M

W)

(a) (b)

1.5 2 2.5 3–400

–300

–200

–100

0

100

177194

300

400

Time (s)

DC

Po

wer

(M

W)

PDC1PDC2PDCinj

(c)

Figure 11. DC power response: a) no injection, b) injection (161 MW) below the limit, c) injection (194 MW) above

the limit.

5.2. AC-side transient stability response

From Figure 13, it is observed that the load angle oscillates during the fault condition period and during the

period that the breaker opens.

1848


1.5 1.8 1.9 2 2.5 2.8 3250

300

323

333337340

347

372

400

Time (s)

UD

C (

kV

)

UDC1

UDC2

1.5 2 2.5 3250

300

333

343348

367

373

400

Time (s)

UD

C (

kV

)

(a) (b)

1.6 1.8 2 2.2 2.4 2.6 2.8 3250

300

350

365371375381387

400

Time (s)

UD

C (

kV

)

UDC1UDC2UDCinj

(c)

Figure 12. DC bus voltage response: a) no injection, b) injection (161 MW) below the limit, c) injection (194 MW)

above the limit.

However, when the breaker closes at 2 s, the load angle oscillates and is damped faster during the injection

scenario, hence improving the transient stability.

1849


1.8 2 2.2 2.4 2.6 2.8 3–500

0

500

Time (s)

UP

CC

2 (k

V)

1.8 2 2.2 2.4 2.6 2.8 3250

300

350

400

Time (s)

UP

CC

1 rm

s (k

V)

1.8 2 2.2 2.4 2.6 2.8 30

101720

30

40

50

Time (s)

Del

ta2

(deg

rees

)

1.8 2 2.2 2.4 2.6 2.8 3–500

0

500

Time (s)

UP

CC

2 (k

V)

1.8 2 2.2 2.4 2.6 2.8 3250

300

350

400

Time (s)

UP

CC

2 rm

s (k

V)

1.8 2 2.2 2.4 2.6 2.8 30

11

20

30

40

Time (s)

Del

ta2

(deg

rees

)

(a) (b)

1.8 2 2.2 2.4 2.6 2.8 3–500

0

500

Time (s)

UP

CC

2 (k

V)

1.8 2 2.2 2.4 2.6 2.8 3250

300

350

400

Time (s)

UP

CC

2 rm

s (k

V)

1.8 2 2.2 2.4 2.6 2.8 30

10

20

30

40

Time (s)

Dle

ta2

(deg

rees

)

(c)

Figure 13. Station 2 UPCC and load angle: : a) no injection, b) injection below the limit, c) injection above the limit.

6. Conclusion

This paper presented the use of a DC-link of an embedded VSC HVDC transmission corridor to enhance the

transient stability of an AC network by DC power injection on the DC-link. VSCs are vulnerable to DC cable

short-circuits and ground faults due to the high discharge current from the DC-link capacitance. A DC line-

to-earth fault results in a high DC fault current and blocks the VSC IGBTs, and hence the voltage source acts

like an uncontrolled rectifier, which results in a rise in the AC fault current. In the analysis, a VSC HVDC

1850


transmission having DC power injection on the DC-transmission corridor was modeled in the time domain.

The zero-input zero-state (ZIZS) response was used to find the solution of the state-space representation. The

system was also modeled in the MATLAB/Simulink environment. The results show that the power injection

created an additional damping of the postfault oscillations of the AC-side power angle and the DC-side voltage

and power oscillations, hence enhancing transient stability.

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